Maths (commerce) Solve the following Question.(1 Marks)

$\lim _{x \rightarrow 0}\left[\frac{\log (1+9 x)}{x}\right]$

$\lim _{x \rightarrow 0}\left(1+\frac{x}{5}\right)^{\frac{1}{x}}$

$\lim _{x \rightarrow 0}\left[\frac{5^x-1}{x}\right]$

$\lim _{x \rightarrow 4}\left[\frac{3-\sqrt{5+x}}{1-\sqrt{5-x}}\right]$

$\lim _{x \rightarrow 0} \frac{(1+x)^n-1}{x}$

If $\lim _{x \rightarrow 2} \frac{x^n-2^n}{x-2}=80$ then find the value of $\mathrm{n}$.

$\lim _{x \rightarrow 2}\left[\frac{x^3-4 x^2+4 x}{x^2-1}\right]$

$\lim _{u \rightarrow 1}\left[\frac{u^4-1}{u^3-1}\right]$

$\lim _{x \rightarrow-2}\left[\frac{-2 x-4}{x^3+2 x^2}\right]$

$\lim _{y \rightarrow 0}\left[\frac{5 y^3+8 y^2}{3 y^4-16 y^2}\right]$

$\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$

$\lim _{z \rightarrow 2}\left[\frac{z^2-5 z+6}{z^2-4}\right]$

If $\lim _{x \rightarrow 1}\left[\frac{x^4-1}{x-1}\right]=\lim _{x \rightarrow a}\left[\frac{x^3-a^3}{x-a}\right]$, find all possible values of a.

$\lim _{x \rightarrow 2}\left[\frac{x^{-3}-2^{-3}}{x-2}\right]$

$\lim _{x \rightarrow 3}\left[\frac{\sqrt{x+6}}{x}\right]$